WASHINGTON—A long-running congressional battle over privacy and surveillance ended Tuesday when the Senate voted to curb the collection of millions of Americans’ phone records, the first significant retrenchment of government spying powers since the 9/11 attacks.

The measure, which was signed Tuesday night by President Barack Obama, will reauthorize and reboot the provisions of the USA Patriot Act that lapsed Sunday at midnight, but it will phase out the National Security Agency’s bulk phone-records program.

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